The 2013 SFU Symposium on Mathematics and Computation was a showcase of research in computational mathematics at SFU, UBC, and UVic.
Program Schedule
Date: Wednesday, August 7th, 2013 Location: The IRMACS Centre, Simon Fraser University
Time | Event or Speaker | Title of Talk |
---|---|---|
9:00am | Registration and Welcome Coffee |
|
9:30am | Lily Yen (Capilano) |
Automation for the generating series of coloured set partitions |
10:15am |
Pavol Hell (SFU) | |
11:00am | Morning Coffee and Poster Setup | |
11:15am | Poster Session and Judging | |
12:15pm | Buffet Lunch |
|
1:15pm | Alexandre Bouchard-Côté (UBC) | Inference algorithms for continuous time Markov chains over large state spaces |
2:00pm | Roberto Armenta (SFU) |
High-Order Finite-Difference Methods for Modelling Electromagnetic Wave Propagation |
2:45pm | Afternoon Coffee | |
3:00pm | Robert Bridson (UBC) | Simulating Smoke without Volumes |
3:45pm | Award Ceremony | Awards for Putnam participants, Undergraduate Research Prize recipients, Operations Research Team Award, and Poster Prizes. |
4:15pm | Poster Presentations by Award Winners | |
4:30pm | Closing Remarks |
High-Order Finite-Difference Methods for Modelling Electromagnetic Wave Propagation
Finite-difference methods are a popular choice for solving systems of partial differential equations (PDEs) numerically. Throughout my work, I employ finite-difference methods to solve the various systems of PDEs that arise in common electromagnetic problems. One of the most important recent developments in finite-difference methods has been the use of finite-difference approximations with an increasable order of accuracy. The ability to increase the order of accuracy of the employed approximations can considerably improve performance; however, to exploit high-order approximations effectively, it is necessary to clearly understand how to incorporate boundary conditions. This issue, which stands as the biggest barrier to the widespread adoption of high-order methods, will be the subject of the talk.
Simulating Smoke without Volumes
In computer graphics, and visual effects in particular, smoke simulation has become a standard tool. Typically it is modeled with incompressible fluid flow on a 3D grid, tracking soot concentration and velocity in the air, and calculating buoyancy and pressure forces to evolve it forward; volume renderers can take the soot concentration as input to produce the final images. However, this doesn't scale very well, particularly to real-time applications like video games where even the volume rendering alone is unacceptably expensive relative to the rest of the application. This calls for a little more mathematical analysis and algorithmic creativity! In many circumstances, we can model the soot concentration as uniformly smoky inside a region sharply bounded by a dynamically evolving surface; vorticity likewise provides a much more efficient representation of the velocity field. Avoiding any use of volume data, we can get to interactive simulation and highly efficient real-time rendering.
Inference algorithms for continuous time Markov chains over large state spaces
Continuous time Markov chains (CTMCs) is a fundamental modeling tool in time series analysis, phylogenetics and many other areas of statistics. In most applications, simplifying assumptions are typically made to reduce the state space of the CTMCs to a finite and typically small collection of objects (in phylogenetics, for example, the four nucleotides). However, new questions and new data types motivate the development of CTMCs over strings, graphs and other countably infinite spaces. In this talk, I will describe some of our recent work on models and algorithms for analyzing CTMCs over countably infinite space. The first part of the talk will be devoted to the Poisson Indel Process, a model for string-valued CTMCs, and the second part, on inference on CTMCs over other countably infinite spaces. I will focus on applications in phylogenetics, but many of the algorithms and models have potential uses in other branches of applied statistics.
Combinatorial dichotomy classifications
In classifying the complexity of certain homomorphism problems, it sometimes turns out that it is the presence of a combinatorial obstruction in the target structure that causes a problem to become intractable. I will discuss several recent results of this type, including recent joint work with Egri, Larose, and Rafiey.
Automation for the generating series of coloured set partitions
The equidistribution of many crossing and nesting statistics exists in several combinatorial objects like matchings, set partitions, permutations, and embedded labelled graphs. The enumeration of such objects according to their crossing or nesting number has been a challenge, often resulting in hard to solve functional equations. When both nesting and crossing numbers are bounded, the generating series are rational for (arc-)colouredmatchings, set partitions, and permutations shown by Chen and Guo, Marberg, and Yen respective. We describe algorithms implemented in Maple that give the rational generating series for non-crossing, non-nesting, c-coloured set partitions and permutations. The success of the implementation leads to the possibility of automation for more complicated structures and provides new directions of attack for previously unsolved functional equations.
The SFU Mathematics Department invites undergraduate and graduate research students, postdoctoral fellows and faculty members to participate in the 2013 SFU Symposium on Mathematics and Computation Poster Session.
The only requirement is that the poster has mathematics in it. It may be applied, pure, computational or experimental mathematics. If you have already prepared a poster for a presentation at another scientific meeting this year, and you would like to present it to members of the Department, this is an appropriate venue. If you wish to present a computer demo this is also possible.
There will be one prize of $200 (winner) and one prize of $100 (runner-up) for the best undergraduate poster, and one prize of $200 (winner) and one prize of $100 (runner-up) for the best graduate poster. Judging will be based on both content and presentation.
Poster titles must be submitted via the online registration form by August 1st, 2013. Presenters are responsible for printing their own poster.
The posters will be displayed in the IRMACS atrium. Poster presenters can set up their posters as early as 9:00am on August 7th, 2013. The poster and demo session will take place from 11:15am to 1:15pm. Awards will be made at 4:30pm, followed by a presentation of the winning undergraduate and winning graduate poster.
Name | Affiliation | Poster Title |
---|---|---|
Lee Safranek | SFU | Diffusion Geometry |
Wei Chen | Simon Fraser University Department of Mathematics | Determinants of Matrices With Polynomial Entries |
Lily Yen | Capilano University and Simon Fraser University | Crossings and Nestings for Arc-coloured permutations |
Avery Beardmore | Simon Fraser University | Boltzmann sampling of gene tree/species tree reconciliations |
Ashok Rajaraman | Department of Mathematics, Simon Fraser University | Assembly of the Black Death agent genome |
Colin Exley | Simon Fraser University | An Agent Based Approach to Modelling Chronic Oenders |
Layla Trummer | NSERC USRA, Dept of Mathematics, Simon Fraser University | Algorithms for the Minimum Distance of Linear Codes |
Graham Banero | SFU | Additive Complexity of Infinite Words |
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